The Costa Rican international has been strongly linked with a move to Los Blancos in recent days, with the Champions League winners believed to lead the race for the stopper.
Navas has insisted that he remains a Levante player, but has hinted that a transfer is in the offing.
"I hope I can speak to you differently in the future and tell you my situation, I hope things go well and can be finalised, but so far, I haven't signed anything with anyone. At the moment, we're still waiting, things are moving along," Inside Spanish Football quotes Navas as saying.
Bayern Munich have also been linked with a move.